Two-dimensional architected materials are often realized as periodic grids of elastic beams. Conventional homogenization methods represent these structures as equivalent elastic solids but neglect shear deformation in the constituent beams. This article addresses this limitation by incorporating shear deformability through Timoshenko beam theory, enabling accurate modeling of stubby beams. Moreover, shearable beams with extreme mechanical characteristics can be obtained through the design of appropriate microstructures. Introducing shearable beams into the grid expands the design space, allowing, for instance, the control of the effective Poisson's ratio beyond the limits achievable with slender beams.

32 pages, 30 figures